Sometimes people say that water is removed from clothes in a spin dru5o;/kfs6 ah dd3g ,lbri*:ttyer by centrifugal force throwing the water outward. What is wu sdr;oh3t5g6bif, kt/:d *larong with this statement?

Will the acceleration of a car be the same5 hsl 1f29mhve when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expef9v5lmh2s h1 lain.

Suppose a car moves at constan sv,cy xqar9* 2whsc7iw364xo t speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level staxs2icr,ywv3shc4 o9 6 xqw* 7retch near the bottom of a hill?

Describe all the forces acting on a chiltfcrf xa )2w6ixm,uq g.b1/v0 ur. p5ad riding a horse on a merry-go-round. Which of these forc/ .txgcmfwfi1 upu,qv 5 .b2x 0ar)ar6es provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingpmtv586ld d at rkm+-1 out, l k-5pmrmd d t1a86+tveven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thrph z*zxdcd(5up8sf pqpl 6 )02ee controls in the car which can be used t*0 zh5s2pl()f 8q pd 6puxpzcdo cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ofnr (m7l t4vn-l a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over rl(7vmt-l n n4the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roue7yy1gq ;:*vfc+x/o/ph s zr jnding a curve at high speed?

Why do airplanes bank wqdf,w 9- ( ciktzpv-m6hen they turn? How would you compute the banking angle given its speed and radiuzcpi6- vd ,-ftw(qm9 ks of the turn?

A girl is whirling a ball on a string around her headoq08m n 5rlbcxih1,4i in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the stringrox5bn 8cm4qih1, l 0i?

Does an apple exert a gravitati, uw yogkhp43jw-pqy+r,j: y- onal force on the Earth? If so, how large a force? C3rk,g-ou-wjy yp:ypjq h+,4w onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wered*h ,q2 *gn akbf 3vf nr+l:jj)c)fs+h double what it is, in what ways would the Moon’s orbit be different?cfl3 fgh+svd2)aj+n)q:jh*f rn,k b *

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thete25zg 8fx 4wg Earth? Which accelerates more4g x5tzw28 efg?

The Sun's gravitational pul,w 1;p3l m bsucal6n:el on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatlaw 61lcm3es;bp,u :nional pull from one side of the Earth to the other.]

Will an object weigh more 8 ;q z.;knhdadat the equator or at the poles? What two effects are aqa; ;8dhkz.dnt work? Do they oppose each other?

The gravitational force on the Moobezgj1n : kw23cr 47c q6nf0fpn due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t ck1n z gr3:cbf6072jnpewf4 q the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sl8)erlk,+izv k s9gb ,mlk8zsie ,rk+v9, gl) baller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towaf z2 umsr+91 usp.lahshjo8vy9v02*o rd the east or (b) toward .oys8hv jl +9* u2o2hp0z9u1marvfssthe west? Consider the Earth’s rotation direction.

When will your apparent weight benjlxdtw:b4t o0;2 nb* the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be;w 4 : 0o*jndtnlxbbt2 the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in *r* o::yzt65x goqmxeouter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like 6zy5rxgoo* t :: *xmeqa cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exp6l *-w+x +wenzvj8bs9dirm*ceriences “free fall” or “apparent weightlessness” between vdcn 8ebjw6 rl++s*ix 9 -zm*wsteps.

The Earth moves faster in its orbit around the Sun o : ;ce/fvcg7nin January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tie:g;n v7co c/flt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untiltu(ggf iea84k 9lz72b it was discovered to have a moon. Explain how this discovery e4 l 7gi9 bgatzf8k(u2enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. w;vdod+ y ds6waa .h( c*+nxe9Yet the Moon's is mainly responsible for t;(6+ho+xday e.vcs* d dw9nw ahe tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198.r k6( u *obh+no/mzpmu-c5 -qnadfd )0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripeta(djhntnjbb2,oa ey oq2 .7h5)l acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assum(jdb.ny2n,q7 ahotjho 52) e be that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-k(z ub 9tcp 5.gher; s0x fg7n;/me*v w+4pxnglg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radiusgf ;p*.v m+ 79bpne;gnuc(0e4thrz5gs / wxlx 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cir7 i+o;4kj2w 3e d3jac xc bgbxf1p9wt3cles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acc a3i b9bfwx4k7jw;co13p3j edctxg+2eleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge9 ,/5aq9rpe xdyga/ek of a potter’s wheel turning at 45 rpm (revolutions per , k9x/r/9apq eg y5aedminute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved a)aot0vcf9 7vwt a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spao9 0cvw 7t)fveed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050l8teoszm(7ysht .))h 5c(g bk-kg car can round a turn of radius 77 m on a flat road if the coefficient of sy)5 o)hk shtml 7g8tec(.bz( static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic ipxm8o8r 6it yl04ds;ient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m ysl i06 8mpo8drxi;t4 at a speed of 95km/h ?   

  A device for training astronauts ado qoas(e 3p:l;s t*n7nd jet fighter pilots is designed to rotate a dpsoa:7l*;3nes q(o t trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a 6ot k v29cixj(0yvm :orotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides ik cmv o6vo92(t:y0xjoff. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be t rkk,5c2z vq udbz6,)jraveling when upside down at the b q kc)vrzkz52d6, ,jutop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the round;20ilx1xcq)drw aio0 w r:iu n*x,ts1oekl/ 8 ed top of a hi8es1a 2tui,rq:irc1lo x/i0;xxo*l )w nd 0wkll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diametefqet :xf :f 1qld9l)kj6 hgb;.r Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?l: d:;tqhjxlgbk1 fe6q.f9f)    rpm

  A bucket of mass 2.00 kg iq32zgrtnz;z m( 5q- rv1kz5kys whirled in a vertical circle of radius 1.10 m. At the lowest poi-z k5tr ;nqz1r k5m3zqv( gz2ynt of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the ax rjauc8b5:-, bsbmdk /+j m.nce //fibis of rotation is to experience an ac bam+ fb/k/rd, i5uc8bj/sj-n.c e b:mceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniv yac+zwm-e,ah1cij8ju.1-y vaf )8hl al, people are rotated in a cylindrically walled "room." (Sj+zch-ie v myf- .1jc 8a8hy)alu,aw1ee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a cirnt bo oq7mb,6s ah *;2cxcm/w)cle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to am7 o*mncoas; bc/b6tqw2, hx) dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of th3(2,h x:szkjmnhgt* qe ball which revolves on a string 0.600 m long. In par:mt, (23gkx h*hqn sjzticular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly bankedo,;;oivt7x7v4mv o;z *q2 vyrsa n,qt for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses9 ./x egc4u hefruo9,m $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by ovm5uw7+ hfcm0xllk8 b8u8 )hdiving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted o oh:f) vu yg 6pdqc:*)nte,/aon the car (by the ground) in Example 5-8 when it oov): ha)*e/6tyd :pnugfq,cs speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unif/j ygwwj:ez5 px8o+m , d8glt3ormly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of zojx3wl t,pgeg dj885ym/+w: static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of ra,t *5/ra j ,t.e lfc6sex i3ro lglz)xtpie:.6dius 2.90 m . At a particular instant, its acceleration is 6:) x.ei *r35,c zlp.tj6loei lras/,gttfxe 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on c noklq7o pm(d8zr g8)u5p*ymsl509e a spacecraft 12,800 km (2 Earth radii) oq5g pn78 pr*lo(su8zkm l)5 ecd 90ymabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerqfv(bsxxj-2 4nz v/ 3uation g has a magnitude of 1x3s 2 qj4uxbn vf-zv(/2 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due o. x3(x- ltzuk/ckc9hk d )ec6to gravity on the Moon. The Moon's radius is 1.74 cte lk-(khcz6d.c3k/ox)9xu $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same ma;ajr fe)vvm 5ggxj75 -ss.g7; frm5gvexav)-j5j What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E ht)oy9 n:xiu -uo8buu8k*l g5chl5,.p/la yjarth, but the same radius. What is g nhnut j)gxuli oc,ok5p8l- l589 y*a/. :ubyh uear its surface?   

  Two objects attract eaab(lbc cpf .8le qce8n1k7 8+kch other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity,g , jf*eh9n/ysl m:an4s 8ah)l at (a) 3200 m lhhs8sje )* fln,n: y9a/am4g   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s m4:qlhtj7yx) p5q+4r u2bffyyur* v8center to a point outside the Earth where thegra8yj2 v4fr*u4y:tm5yfrhx+l b qu 7p)q vitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fig4 ,pthn3f u(nc azua-nr 60p*ve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfa(0paanrg*-uhu fnn3 ,4 t6pzc ce gravity on this monster.    $\times10^12$

  A typical white-dwarf o0e j q6**wvz) k5yx1asksl+ rstar, which once was an average star like our Sun but is nols6v*0o yz 1w5k)axr e+sj q*kw in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless w*bh 6lrl*w5xg 49n dsp jswtvv3j8-f osw10*qhile orbiting in the space shuttle. Your friends respond that they thought gravity was*sn0wjfl9j3w8q gx54pr 6*twv1-old svbs*h just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square6d*v(y/kgj6ae ta d; h of side 0.60 m. Calculate the magnitude and dha(6;j gyadd* k6tv /eirection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pla:kd5 7s ehdtv0ufol0a g+p/9wnets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, a:/5tudhws7da ov+pk 0ge9f l0 ssuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceler780j8i8uu*xxmktobu ation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius 07ubx8 8 uikm uoxj8t*is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val)wte/l)3*amx6 tmk zx ue for the period of the Earth and its distance from the Sun. [Note: Compare your answer toxt)w kxl3zmae*/ )6mt that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite m/fb f /b*tvw4toving in a stable circular orbit about the Earth at 4v *f tb/bftw/a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 ucyzjd 0t7g-(f56cz ukm above the Earth. How fast must the shuttle be moving (relative to Earth) when 7u5f yc d 06(ucztzjg-the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to ex+s9ja;hvt m9wkt,wk 9 perience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 3 9tw9kmv +tjk9s;awh, 2 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circulayk r+k1henwgf* h9* h( q r:ntllk/ak/a* p02nr “near-Earth” orbit. A “near-Earth” orbit is one at a hei* /n+2hknlph 1ft w:k k09*hqa*/(neklyrargght above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top ozd3o:t gv(a :wf Mt. Everest to be placed in a circular dt(:ow3: vzag orbit around the Earth?   

  During an Apollo lunar landing mission, the command m36t w y wvce/gc txtaw1z31m5,odule continued to orbit the Moon at an altitude of about 100 km. How long did it takemz3yw1, te1avt gx36/5 w wcct to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Tkah :/,)c i8un ru0 1ahkaia*ohe inner radius of tok r0 hhc an,aa8uu*i/i)1:kahe rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in dia xlfway 0g8o-,zwlzr7u dp),yd8dy02meter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a persowg0y7o dzl)y,8zxu0y8 ld pdfwr 2-a,n’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from tc s 4wfaenm()1(*isq7*s ce vnhe center of the Earth's Moon**icenaev m7( 4ss1s qn(cwf) in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equazai 83uqh60e*x 6 wmdt3/lqwfl mass. They are observed to be separahel660*3u8tq q wizaxwm d/f3ted by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5 mc+,a n5ih- gmvy/fp95-kg woman in an elevator that moves h+/f-a9giyp5vcn, m m
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator*,*me6 yv+-rn dkz xcz. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minim,cyk6x-rv * +mz*znd eum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near theq 90,e/is,qf mhdy we* surface of a planet with period T , the density (mass/volume) of the planet i,d/0*y qf,iesh wmqe9s $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to de2iia.9k3p* gzzs j sxcx96(cxtermine the period of an artificial satellite orbiting very ni 9kc6sx.3xp zz(x cjsi9*2gaear the Earth’s surface.    s

  The asteroid Icarus, though only+y h+3c 9oqbc ws 2/bl/lnfvf33o4f ji a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fro3+3v4 lf2f3jboy w lo //f9bscqi+cnhm the Sun?    $\times 10^{11}$

  Neptune is an average distatltfa;* eub x3c,fu49 nce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Suk i-bi*yn cmsd1h5 ;h.n roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is. *5nch;yhkdbi 1- mis nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abou2 :pcwo ;4p2cf74vxg7ioj afft the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fvy: 9fnj)145qfte 6yfsr5j ysour largest moons of Jupiter (those discovered by Galileo inj51tq6vy effys ns fj5:49r)y 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known peri12sc 8rttrz *iod and distance of the Moon. sz21ct8ri r*t    $\times 10^{24}$

  Determine the mean distance from Jupiter for eacoo7l*mg m3t6evlw0c7 h of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Comvo0wm g3 7oem *ltl6c7pare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whj0k:3;u s jo;7x7fm*m/lsrqtgyw 9o o ich some space scientists think came from a planet that once orbited the Sun but wasywo0 3s9mx lqmf7t u;o/jj ;k:*ros 7g destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a b4( bl(czdep5e66vp:d pl9 s srand completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on E(5l( spbdr6pvpz4 ee:s6 9cldarth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swingjac kkp:b/-cf6n8 /ri0/idommfce ;6ing in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest pointk /ck-0m o 6jd/ p8ba6cifnmf:;erc/i of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will q 0xyi+ 4ucqnq+ fk;di8ce0q6w,o;eg the acceleration of gravity be half what it iu 0q 48nq +oiicd;cxqee6yg+f 0wk ;,qs on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mut2a*7*0tyq-h ;dn a z;pcmlnyhual circle once every 2.5 s. If we assume their arms ar* hyzlq2pd0 7tnm*; a;na -yche each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acce+1r*fw nm6 4n1 tde3llbyj2kqleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of yl3f61lq+nmdj4bne 1 *twrk 2 this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from thel792facq*gu+ql y*uc Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and o uqalc +fql9*gc*u 27ypposite forces?    $\times 10^8$

  You know your mass is 65oqtn ga3v8ea 5,mm5u8 kg, but when you stand on a bathroom scale in an elevator, it saoa5e 8m3qu n,v85mg atys your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotjynwhzc ;jybsc )gql 3j sq701-86q4r ate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is6hjysj bj)sw0gq4qq7l31z8n;y - ccr to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aijb,( uj qy8lqmich/)1rcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in termhl(zqr/. i )u)w s+ttxs of its radius r, the acceleration due to gsqi)zwu/(h t+ t)x.l rravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) isebm/3, nl,kl h2k h j05xkb,fl deflected from the vertical by an ,/n, 5ehm h kll03,bkf2blxkjangle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m isfvasba9utf 1eds /t+lco9 0;2 banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a ca t;02 fatulfed+91s9 s/cvaobr safely handle the curve?

  How long would a day be if the Earthr5 ou3s5-c/opj,h f:p f yae0u were rotating so fast that objects at the equator were apf /yo0jp h5ue-3r5,usa:c fp oparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a f7wagf -jeg2 ,f6uy) yconstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radiujhbdaa2y))7c*s / yt ws 235 m. A lamp suspended from the ceiling swings out to an angle o waj dbts*)/2)cy7hayf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as 6weaxqwp8dq 85jb ;k-massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of sucxkedj8-wq 8; pqbaw56h a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope dedufwjbh +l 6vk-bhw t9( e71an0dced the presence of an extremely massive core in the distant galaxy M87, so dense th h90dj albew6t -knvwb+ f(71hat it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hi6+vm s hvpbiv5 l4nhg3c-:kf cc0z 99oll and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. :h4 6v9zc9ng c3m +i-ovc v0bklpfh5s (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilize*ug7h w0pr83 ;zfqx68eytjuymq4 jd1s a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites i1f;duug hw pyq46x q7re8mjt yj8*0z3n each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmu xdejv+ dvk-(a4c,6q, is meant dqjad 6,c vexv+k(-u 4to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repanta72hrrqs(0 pv1(yj ir. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km beryp n7r taj(10qh2s(vhind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp hau.a q8 qicmu(/s a period of 3000 years. (a) What is its mean distance from the /.uau q(c8miqSun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "felly h31sff:77yxf h 6hel" yourself gravitat1h6hhly3 lxsf 7f :fy7ionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around 1qvk nv 8;g ly(kyw,u1the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center 81yv u,n (k;qw1 vklgy$ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5z *vaaccfs52:9s n9or 0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom 9 *rf n25acs:sovc za9side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550 o+,g/hcg m ri/a/w scbc:4x.s0 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swed,4tr1 ldmf by9) lv)q,wk)exep second hand on your wrist wa14vy ml rwedb),)k ,fdtqxl9) tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arouvh *8supsi,u 6f .)d7au q5shdnd in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fi *ud6pqa 8h,)ui ssd.7v5hufsg. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed+ n1 - hacvqgw6);u h6-o w.yfzebyy/9isb(as so that a car traveliyunia 9 +w;h fgsyv. b6)soe6qwc 1ahz-yb/ -(ng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when:,mkzte +-t) nhdk6f o negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds de:n+ t ktf),6-omhkz a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$